Sun Shin Ahn’s research while affiliated with Dongguk University and other places

Using the notion of the Łukasiewicz fuzzy set, we study the filter theory of Sheffer stroke Hilbert algebras. Here’s what we’re trying to do. 1. We first introduce the Łukasiewicz fuzzy filter of Sheffer stroke Hilbert algebras. 2. We provide an example to illustrates the Łukasiewicz fuzzy filter. 3. We examine the various properties of the Łukasiewicz fuzzy filter. 4. We discuss characterizations of the Łukasiewicz fuzzy filter. 5. We explore the conditions under which Łukasiewicz fuzzy set can be Łukasiewicz fuzzy filter. 6. We discuss the relationship between fuzzy filter and Łukasiewicz fuzzy filter. 7. We use the given filter to creates a Łukasiewicz fuzzy filter. 8. We present conditions for the three subsets, called ∈-set, q-set and O-set, to be filters.

Some kinds of pseudo valuations such as positive implicative pseudo valuation, (weak) implicative pseudo valuation, and commutative pseudo valuation of various types are introduced. Several examples, properties and characterizations of them are given as well. The relationships between them and the substructures of hyper BCK -algebras are investigated, too. Finally, by giving various examples and theorems, the relationships among the proposed pseudo valuations are investigated and characterized, especially in hyper BCK -algebras with three elements.

In this paper, we introduce the notion of generalized anti-symmetry laws in groupoids, and we apply this concept to several algebraic structures. Moreover, we show that every Fibonacci sequence on ( C , *) is periodic.

To investigate the filter and deductive system of the Schaefer stroke Hilbert algebra using the Dokdo structure, the concept of Dokdo filter and Dokdo deductive system is defined, examples are given, and various properties are investigated. The Dokdo filter is formed by attaching appropriate conditions to the given Dokdo structure. The characterization of Dokdo filter is studied. Dokdo filters related to filters are constructed. Dokdo filter and Dokdo deductive system turn out to be the same concept.

Based on the concept of fuzzy points, the notion of a prominent fuzzy GE-filter is defined, and the various properties involved are investigated. The relationship between a fuzzy GE-filter and a prominent fuzzy GE-filter is discussed, and the characterization of a prominent fuzzy GE-filter is considered. The conditions under which a fuzzy GE-filter can be a prominent fuzzy GE-filter are explored, and conditions for the trivial fuzzy GE-filter to be a prominent fuzzy GE-filter are provided. The conditions under which the ∈t-set and Qt-set can be prominent GE-filters are explored. Finally, the extension property for the prominent fuzzy GE-filter is discussed.

With the aim of applying the Dokdo structure to BE-algebra, the notions of (weak) Dokdo BE-subalgebra and Dokdo BE-filter are introduced, and their properties are investigated. The relationship between weak Dokdo BE-subalgebra, Dokdo BE-subalgebra and Dokdo BE-filter is established. The conditions under which Dokdo structure can be weak Dokdo BE-subalgebra and Dokdo BE-filter,and the condition under which weak Dokdo BE-subalgebra can be Dokdo BE-subalgebra are explored. Characterizations of Dokdo BE-filter are provided.

In this paper, the notions of normal m-dominating set, normal m-domination number, inverse normal domination set (number) and inverse normal m-domination number are introduced, and some the related results are investigated. Finally, a utilization relevant to decision-making based on influencing factors the company’s efficiency is presented.

For the purpose of applying the concept of Lukasiewicz fuzzy set to ideals in BE-algebras, Lukasiewicz fuzzy ideal is introduced, and its properties are studied. The relationship between fuzzy ideal and Lukasiewicz fuzzy ideal is discussed. Conditions for the Lukasiewicz fuzzy set to be a Lukasiewicz fuzzy ideal are provided, and characterizations of Lukasiewicz fuzzy ideal are displayed. Conditions in which three subsets, called ∈-set, q-set and O-set, are ideals are explored.

By applying the concept of Lukasiewicz fuzzy set to BE-algebras, the notions of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are introduced, and their properties are investigated. Characterizations of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are discussed, and the relationship between fuzzy BE-algebra (resp., fuzzy BE-filter) and Lukasiewicz fuzzy BE-algebra (resp., Lukasiewicz fuzzy BE-filter) is established. The conditions for the ∈-set, q-set and O-set of Lukasiewicz fuzzy set to be BE-subalgebras are explored. Lukasiewicz fuzzy BE-filter is created by using BE-filter.

In this paper, we introduce the notions of a left and a right idenfunction in a groupoid by using suitable functions, and we apply this concept to several algebraic structures. Especially, we discuss its role in linear groupoids over a field. We show that, given an invertible function $\varphi$, there exists a groupoid such that $\varphi$ is a right idenfunction. The notion of a right pseudo semigroup will be discussed in linear groupoids. The notion of an inversal is a generalization of an inverse element, and it will be discussed with idenfunctions in linear groupoids over a field.